I saw the gross photos and X-ray at the above link, but still have to wonder: Just how could someone lose a ring INSIDE their finger? Did skin grow around it and encase it?
Very strange, but I have to wonder how something like that could happen. The nearest I can figure is that she developed a staph infection (probably from something getting in under the ring and never cleaned out), which caused massive swelling. I'd love to hear a medical explanation though (what's on the site is pretty terse).
The article mentions mxyedema or myxoedema for those addicted to the British spelling. This is associated with profound hypothyroidism (this case), and can cause non-pitting edematous swelling. Possibly the woman's fingers swelled, and she was not mentally capable of caring for herself, the infection set it, and a granuloma formed.
Similar, but not exactly the same: dogs who have a collar placed on them as pups and not properly attended; the collar grows into the neck as the dog grows. Usually presented for foul odor and/or swollen head, usually at 5:30 PM on Friday, usually with the statement "I ain't got no money."